Enhanced puncturing and low-density parity-check (ldpc) code structure

ABSTRACT

Certain aspects of the present disclosure generally relate to techniques for enhanced puncturing and low-density parity-check (LDPC) code structure. A method for wireless communications by a transmitting device is provided. The method generally includes encoding a set of information bits based on a LDPC code to produce a code word, the LDPC code defined by a base matrix having a first number of variable nodes and a second number of check nodes; puncturing the code word according to a puncturing pattern designed to puncture bits corresponding to at least two of the variable nodes to produce a punctured code word; adding at least one additional parity bit for the at least two punctured variable nodes; and transmitting the punctured code word.

CROSS-REFERENCE TO RELATED APPLICATION & PRIORITY CLAIM

This application is a continuation of U.S. patent application Ser. No.15/593,035, filed May 11, 2017, and claims benefit of and priority toU.S. Provisional Patent Application Ser. No. 62/335,163, filed May 12,2016, which is herein incorporated by reference in its entirety for allapplicable purposes.

TECHNICAL FIELD

Certain aspects of the technology discussed below generally relates towireless communications and detecting and/or correcting errors in binarydata and, more particularly, to methods and apparatus for enhancedpuncturing and low-density parity-check (LDPC) code structure. Certainaspects can enable improved performance of the punctured LDPC codes.

INTRODUCTION

Wireless communication systems are widely deployed to provide varioustypes of communication content such as voice, video, data, messaging,broadcasts, and so on. These systems may employ multiple-accesstechnologies capable of supporting communication with multiple users bysharing available system resources (e.g., bandwidth and transmit power).Examples of such multiple-access systems include code division multipleaccess (CDMA) systems, time division multiple access (TDMA) systems,time division synchronous CDMA (TD-SCDMA) systems, frequency divisionmultiple access (FDMA) systems, single-carrier FDMA (SC-FDMA) systems,3^(rd) Generation Partnership Project (3GPP) long term evolution (LTE)systems, LTE Advanced (LTE-A) systems, and orthogonal frequency divisionmultiple access (OFDMA) systems.

Multiple access technologies have been adopted in varioustelecommunication standards to provide a common protocol that enablesdifferent wireless devices to communicate on a municipal, national,regional, and even global level. An example of an emergingtelecommunication standard is new radio (NR), for example, 5G radioaccess. NR is a set of enhancements to the LTE mobile standardpromulgated by 3GPP. It is designed to better support mobile broadbandInternet access by improving spectral efficiency, lowering costs,improving services, making use of new spectrum, and better integratingwith other open standards using OFDMA with a cyclic prefix (CP) on thedownlink (DL) and on the uplink (UL) as well as support beamforming,multiple-input multiple-output (MIMO) antenna technology, and carrieraggregation.

Generally, a wireless multiple-access communication system cansimultaneously support communication for multiple wireless nodes. Eachnode communicates with one or more base stations via transmissions onforward and reverse links. The forward link (or downlink) refers to acommunication link from base stations to nodes, and a reverse link (oruplink) refers to a communication link from nodes to base stations.Communication links may be established via a single-input single-output,multiple-input single-output, or a multiple-input multiple-output (MIMO)system.

A wireless multiple-access communication system may include a number ofBSs, each simultaneously supporting communication for multiplecommunication devices, otherwise known as user equipment (UEs). In anLTE or LTE-A network, a set of one or more BSs may define an e NodeB(eNB). In other examples (e.g., in a next generation, NR, or 5Gnetwork), a wireless multiple access communication system may include anumber of distributed units (DUs) (e.g., edge units (EUs), edge nodes(ENs), radio heads (RHs), smart radio heads (SRHs), transmissionreception points (TRPs), etc.) in communication with a number of centralunits (CUs) (e.g., central nodes (CNs), access node controllers (ANCs),etc.), where a set of one or more DUs, in communication with a CU, maydefine an access node (e.g., a BS, a NR BS, a 5G BS, a NB, an eNB, NRNB, a 5G NB, an access point (AP),), a network node, a gNB, a TRP,etc.). A BS, AN, or DU may communicate with a UE or a set of UEs ondownlink channels (e.g., for transmissions from a BS or to a UE) anduplink channels (e.g., for transmissions from a UE to a BS, AN, or DU).

Binary values (e.g., ones and zeros), are used to represent andcommunicate various types of information, such as video, audio,statistical information, etc. Unfortunately, during storage,transmission, and/or processing of binary data, errors may beunintentionally introduced; for example, a “1” may be changed to a “0”or vice versa.

Generally, in the case of data transmission, a receiver observes eachreceived bit in the presence of noise or distortion and only anindication of the bit's value is obtained. Under these circumstances,the observed values are interpreted as a source of “soft” bits. A softbit indicates a preferred estimate of the bit's value (e.g., a 1 or a 0)together with some indication of the reliability of that estimate. Whilethe number of errors may be relatively low, even a small number oferrors or level of distortion can result in the data being unusable or,in the case of transmission errors, may necessitate re-transmission ofthe data. To provide a mechanism to check for errors and, in some cases,to correct errors, binary data can be coded to introduce carefullydesigned redundancy. Coding of a unit of data produces what is commonlyreferred to as a codeword. Because of its redundancy, a codeword willoften include more bits than the input unit of data from which thecodeword was produced.

Redundant bits are added by an encoder to the transmitted bitstream tocreate a codeword. When signals arising from transmitted codewords arereceived or processed, the redundant information included in thecodeword as observed in the signal can be used to identify and/orcorrect errors in or remove distortion from the received signal in orderto recover the original data unit. Such error checking and/or correctingcan be implemented as part of a decoding process. In the absence oferrors, or in the case of correctable errors or distortion, decoding canbe used to recover from the source data being processed, the originaldata unit that was encoded. In the case of unrecoverable errors, thedecoding process may produce some indication that the original datacannot be fully recovered. Such indications of decoding failure caninitiate retransmission of the data. As the use of fiber optic lines fordata communication and the rate at which data can be read from andstored to data storage devices (e.g., disk drives, tapes, etc.)increases, there is an increasing need for efficient use of data storageand transmission capacity but also for the ability to encode and decodedata at high rates.

BRIEF SUMMARY

The following summarizes some aspects of the present disclosure toprovide a basic understanding of the discussed technology. This summaryis not an extensive overview of all contemplated features of thedisclosure, and is intended neither to identify key or critical elementsof all aspects of the disclosure nor to delineate the scope of any orall aspects of the disclosure. Its sole purpose is to present someconcepts of one or more aspects of the disclosure in summary form as aprelude to the more detailed description that is presented later. Afterconsidering this discussion, and particularly after reading the sectionentitled “Detailed Description” one will understand how the features ofthis disclosure provide advantages that include improved communicationsbetween access points and stations in a wireless network.

While encoding efficiency and high data rates are important, for anencoding and/or decoding system to be practical for use in a wide rangeof devices (e.g., consumer devices), it is also important that theencoders and/or decoders can be implemented at reasonable cost.

As the demand for mobile broadband access continues to increase, thereexists a need for further improvements in NR technology. Preferably,these improvements should be applicable to other multi-accesstechnologies and the telecommunication standards that employ thesetechnologies. One area for improvements is the area ofencoding/decoding, applicable to NR. For example, techniques for highperformance LDPC codes for NR are desirable.

Certain aspects of the present disclosure generally relate to methodsand apparatus for enhanced puncturing of low-density parity-check (LDPC)codes. Communication systems often need to operate at several differentrates. LDPC codes are one option for a simple implementation thatprovides coding and decoding at different rates. For example,higher-rate LDPC codes can be generated by puncturing lower-rate LDPCcodes.

Certain aspects of the present disclosure provide a method for wirelesscommunications that may be performed by a transmitting device. Themethod generally includes encoding a set of information bits based on aLDPC code to produce a code word, the LDPC code defined by a base matrixhaving a first number of variable nodes and a second number of checknodes; puncturing the code word according to a puncturing patterndesigned to puncture bits corresponding to at least two of the variablenodes to produce a punctured code word; adding at least one additionalparity bit for the at least two punctured variable nodes; andtransmitting the punctured code word.

Certain aspects of the present disclosure provide an apparatus forwireless communications such as a transmitting device. The apparatusgenerally includes means for encoding a set of information bits based ona LDPC code to produce a code word, the LDPC code defined by a basematrix having a first number of variable nodes and a second number ofcheck nodes; means for puncturing the code word according to apuncturing pattern designed to puncture bits corresponding to at leasttwo of the variable nodes to produce a punctured code word; means foradding at least one additional parity bit for the at least two puncturedvariable nodes; and means for transmitting the punctured code word.

Certain aspects of the present disclosure provide an apparatus forwireless communications such as a transmitting device. The apparatusgenerally includes at least one processor coupled with a memory andconfigured to encode a set of information bits based on a LDPC code toproduce a code word, the LDPC code defined by a base matrix having afirst number of variable nodes and a second number of check nodes;puncture the code word according to a puncturing pattern designed topuncture bits corresponding to at least two of the variable nodes toproduce a punctured code word; and add at least one additional paritybit for the at least two punctured variable nodes. The apparatusincludes a transmitter configured to transmit the punctured code word.

Certain aspects of the present disclosure provide a computer readablemedium having computer executable code stored thereon. The computerexecutable code generally includes code for encoding a set ofinformation bits based on a LDPC code to produce a code word, the LDPCcode defined by a base matrix having a first number of variable nodesand a second number of check nodes; code for puncturing the code wordaccording to a puncturing pattern designed to puncture bitscorresponding to at least two of the variable nodes to produce apunctured code word; code for adding at least one additional parity bitfor the at least two punctured variable nodes; and code for transmittingthe punctured code word.

Other aspects, features, and embodiments of the present disclosure willbecome apparent to those of ordinary skill in the art, upon reviewingthe following description of specific, exemplary aspects of the presentdisclosure in conjunction with the accompanying figures. While featuresof the present disclosure may be discussed relative to certain aspectsand figures below, all aspects of the present disclosure can include oneor more of the advantageous features discussed herein. In other words,while one or more aspects may be discussed as having certainadvantageous features, one or more of such features may also be used inaccordance with the various aspects of the disclosure discussed herein.In similar fashion, while exemplary aspects may be discussed below asdevice, system, or method embodiments it should be understood that suchexemplary embodiments can be implemented in various devices, systems,and methods.

BRIEF DESCRIPTION OF THE DRAWINGS

So that the manner in which the above-recited features of the presentdisclosure can be understood in detail, a more particular description,briefly summarized above, may be had by reference to aspects, some ofwhich are illustrated in the appended drawings. The appended drawingsillustrate only certain typical aspects of this disclosure, however, andare therefore not to be considered limiting of its scope, for thedescription may admit to other equally effective aspects.

FIG. 1 is a block diagram illustrating an example wireless communicationnetwork, in accordance with certain aspects of the present disclosure.

FIG. 2 is a block diagram illustrating an example logical architectureof a distributed radio access network (RAN), in accordance with certainaspects of the present disclosure.

FIG. 3 is a diagram illustrating an example physical architecture of adistributed RAN, in accordance with certain aspects of the presentdisclosure.

FIG. 4 is a block diagram illustrating a design of an example basestation (BS) and user equipment (UE), in accordance with certain aspectsof the present disclosure.

FIG. 5 is a diagram showing examples for implementing a communicationprotocol stack, in accordance with certain aspects of the presentdisclosure.

FIG. 6 illustrates an example of a downlink (DL)-centric subframe, inaccordance with certain aspects of the present disclosure.

FIG. 7 illustrates an example of an uplink (UL)-centric subframe, inaccordance with certain aspects of the present disclosure.

FIG. 8 is a graphical representation of an exemplary low-densityparity-check (LDPC) code, in accordance with certain aspects of thepresent disclosure.

FIG. 8A is a matrix representation of the example LDPC code of FIG. 8,in accordance with certain aspects of the present disclosure.

FIG. 9 is a graphical representation of liftings of the LDPC code ofFIG. 8, in accordance with certain aspects of the present disclosure.

FIG. 10 is an integer representation of a matrix for a quasi-cyclic802.11 LDPC code.

FIG. 11 is a simplified block diagram illustrating an example encoder,in accordance with certain aspects of the present disclosure.

FIG. 12 is a simplified block diagram illustrating an example decoder,in accordance with certain aspects of the present disclosure.

FIG. 13 is a flow diagram illustrating example operations for encodinginformation based on enhanced puncturing and LDPC code structure forwireless communications by a transmitting device, in accordance withcertain aspects of the present disclosure.

FIG. 14 shows a graphical representation of an exemplary LDPC codehaving multiple punctured relatively low-degree variable nodes andadditional parity bits, in accordance with certain aspects of thepresent disclosure.

To facilitate understanding, identical reference numerals have beenused, where possible, to designate identical elements that are common tothe figures. It is contemplated that elements disclosed in oneembodiment may be beneficially utilized on other embodiments withoutspecific recitation.

DETAILED DESCRIPTION

Aspects of the present disclosure provide apparatus, methods, processingsystems, and computer program products for encoding (and/or decoding)for new radio (NR) access technology (e.g., 5G radio access). NR mayrefer to radios configured to operate according to a new air interfaceor fixed transport layer. NR may include support for enhanced mobilebroadband (eMBB) service targeting wide bandwidth (e.g., 80 MHz andbeyond), millimeter wave (mmW) service targeting high carrier frequency(e.g., 60 GHz), massive machine type communications (mMTC) servicetargeting non-backward compatible MTC techniques, and/or missioncritical (MiCr) service targeting ultra-reliable low-latencycommunications (URLLC) service. These services may include latency andreliability requirements. NR may use low-density parity-check (LDPC)coding and/or polar codes.

Aspects of the present disclosure provide techniques for enhancedpuncturing and low-density parity-check (LDPC) code structure, forexample, for LDPC codes with enhanced performance. In aspects, multiplerelatively low-degree variable nodes can be punctured, for example,rather than a single high-degree variable node. The degree of thevariable nodes refers to the number of connections between the variableto check nodes in the base graph. In a large base graph (also referredto as the base code or base PCM), the variable nodes can support ahigher degree of connectivity relative to the variable nodes a smallerbase graph. Additionally, to effectively boost the code rate, extraparity bits can be added to the LDPC code structure, each parity bitcorresponding to a one-degree variable node formed by the parity of thetwo punctured nodes.

Various aspects of the disclosure are described more fully hereinafterwith reference to the accompanying drawings. This disclosure may,however, be embodied in many different forms and should not be construedas limited to any specific structure or function presented throughoutthis disclosure. Rather, these aspects are provided so that thisdisclosure will be thorough and complete, and will fully convey thescope of the disclosure to those skilled in the art. Based on theteachings herein one skilled in the art should appreciate that the scopeof the disclosure is intended to cover any aspect of the disclosuredisclosed herein, whether implemented independently of or combined withany other aspect of the disclosure. For example, an apparatus may beimplemented or a method may be practiced using any number of the aspectsset forth herein. In addition, the scope of the disclosure is intendedto cover such an apparatus or method which is practiced using otherstructure, functionality, or structure and functionality in addition toor other than the various aspects of the disclosure set forth herein. Itshould be understood that any aspect of the disclosure disclosed hereinmay be embodied by one or more elements of a claim. The word “exemplary”is used herein to mean “serving as an example, instance, orillustration.” Any aspect described herein as “exemplary” is notnecessarily to be construed as preferred or advantageous over otheraspects.

Although particular aspects are described herein, many variations andpermutations of these aspects fall within the scope of the disclosure.Although some benefits and advantages of the preferred aspects arementioned, the scope of the disclosure is not intended to be limited toparticular benefits, uses, or objectives. Rather, aspects of thedisclosure are intended to be broadly applicable to different wirelesstechnologies, system configurations, networks, and transmissionprotocols, some of which are illustrated by way of example in thefigures and in the following description of the preferred aspects. Thedetailed description and drawings are merely illustrative of thedisclosure rather than limiting, the scope of the disclosure beingdefined by the appended claims and equivalents thereof.

The techniques described herein may be used for various wirelesscommunication networks such as Code Division Multiple Access (CDMA)networks, Time Division Multiple Access (TDMA) networks, FrequencyDivision Multiple Access (FDMA) networks, Orthogonal FDMA (OFDMA)networks, Single-Carrier FDMA (SC-FDMA) networks, etc. The terms“networks” and “systems” are often used interchangeably. A CDMA networkmay implement a radio technology such as Universal Terrestrial RadioAccess (UTRA), CDMA2000, etc. UTRA includes Wideband-CDMA (W-CDMA) andLow Chip Rate (LCR). CDMA2000 covers IS-2000, IS-95, and IS-856standards. A TDMA network may implement a radio technology such asGlobal System for Mobile Communications (GSM). An OFDMA network mayimplement a radio technology such as Evolved UTRA (E-UTRA), IEEE 802.11,IEEE 802.16, IEEE 802.20, Flash-OFDM®, etc. UTRA, E-UTRA, and GSM arepart of Universal Mobile Telecommunication System (UMTS). 3GPP LTE andLTE-Advanced (LTE-A) are releases of UMTS that use E-UTRA. UTRA, E-UTRA,UMTS, LTE, LTE-A and GSM are described in documents from an organizationnamed “3rd Generation Partnership Project” (3GPP). CDMA2000 is describedin documents from an organization named “3rd Generation PartnershipProject 2” (3GPP2). These communications networks are merely listed asexamples of networks in which the techniques described in thisdisclosure may be applied; however, this disclosure is not limited tothe above-described communications network. For clarity, it is notedthat while aspects may be described herein using terminology commonlyassociated with 3G and/or 4G wireless technologies, aspects of thepresent disclosure can be applied in other generation-basedcommunication systems, such as new radio (NR) technologies including 5Gand later.

Wireless Communication System Context

FIG. 1 illustrates an example wireless communications network 100 inwhich aspects of the present disclosure may be performed. For example, atransmitting device such as UE 120 or a BS 110 can encode a set ofinformation bits based on a low-density parity-check (LDPC) code toproduce a code word. The transmitting device may perform puncturing ofthe LDPC according to a puncturing pattern. The puncturing pattern canbe designed to puncture bits corresponding to at least two of thevariable nodes. The punctured variable nodes can be the highest degreevariable nodes in the base matrix but relatively low degree variablenodes relative to variable nodes in other LDPC codes. High-degreevariable nodes have many connections to the check nodes. Large basegraphs (e.g., having many check nodes) may support/include larger degreevariable nodes relative to small base graphs (e.g., having few checknodes). Extra parity bits can be added to the LDPC code structure foreach pair of punctured variable nodes.

As illustrated in FIG. 1, wireless communications network 100 mayinclude a number of BSs 110 and other network entities. ABS may be astation that communicates with UEs. Each BS 110 may providecommunication coverage for a particular geographic area. In 3GPP, theterm “cell” can refer to a coverage area of a Node B and/or a Node Bsubsystem serving this coverage area, depending on the context in whichthe term is used. In NR systems, the term “cell” and gNB, Node B, 5G NB,AP, NR BS, NR BS, TRP, etc., may be interchangeable. In some examples, acell may not necessarily be stationary, and the geographic area of thecell may move according to the location of a mobile BS. In someexamples, the BSs may be interconnected to one another and/or to one ormore other BSs or network nodes (not shown) in wireless communicationsnetwork 100 through various types of backhaul interfaces such as adirect physical connection, a virtual network, or the like using anysuitable transport network.

In general, any number of wireless networks may be deployed in a givengeographic area. Each wireless network may support a particular radioaccess technology (RAT) and may operate on one or more frequencies. ARAT may also be referred to as a radio technology, an air interface,etc. A frequency may also be referred to as a carrier, a frequencychannel, etc. Each frequency may support a single RAT in a givengeographic area in order to avoid interference between wireless networksof different RATs. In some cases, NR or 5G RAT networks may be deployed.

A BS may provide communication coverage for a macro cell, a pico cell, afemto cell, and/or other types of cell. A macro cell may cover arelatively large geographic area (e.g., several kilometers in radius)and may allow unrestricted access by UEs with service subscription. Apico cell may cover a relatively small geographic area and may allowunrestricted access by UEs with service subscription. A femto cell maycover a relatively small geographic area (e.g., a home) and may allowrestricted access by UEs having association with the femto cell (e.g.,UEs in a Closed Subscriber Group (CSG), UEs for users in the home,etc.). ABS for a macro cell may be referred to as a macro BS. ABS for apico cell may be referred to as a pico BS. A BS for a femto cell may bereferred to as a femto BS or a home BS. In the example shown in FIG. 1,BS 110 a, BS 110 b, and BS 110 c may be macro BSs for the macro cell 102a, macro cell 102 b, and macro cell 102 c, respectively. A BS maysupport one or multiple (e.g., three) cells.

Wireless communications network 100 may also include relay stations. Arelay station is a station that receives a transmission of data and/orother information from an upstream station (e.g., a BS 110 or a UE 120)and sends a transmission of the data and/or other information to adownstream station (e.g., a UE 120 or a BS 110). A relay station mayalso be a UE that relays transmissions for other UEs. In the exampleshown in FIG. 1, relay station 110 r may communicate with BS 110 a andUE 120 r in order to facilitate communication between BS 110 a and UE120 r. A relay station may also be referred to as a relay, a relay eNB,etc.

Wireless communications network 100 may be a heterogeneous network thatincludes BSs of different types, for example, macro BS, pico BS, femtoBS, relays, etc. These different types of BSs may have differenttransmit power levels, different coverage areas, and different impact oninterference in the wireless communications network 100. For example, amacro BS may have a high transmit power level (e.g., 20 Watts) whereaspico BS, femto BS, and relays may have a lower transmit power level(e.g., 1 Watt).

Wireless communications network 100 may support synchronous orasynchronous operation. For synchronous operation, the BSs may havesimilar frame timing, and transmissions from different BSs may beapproximately aligned in time. For asynchronous operation, the BSs mayhave different frame timing, and transmissions from different BSs maynot be aligned in time. The techniques described herein may be used forboth synchronous and asynchronous operation.

Network controller 130 may couple to a set of BSs and providecoordination and control for these BSs. Network controller 130 maycommunicate with BSs 110 via a backhaul. BSs 110 may also communicatewith one another, e.g., directly or indirectly via wireless or wirelinebackhaul.

UEs 120 (e.g., UE 120 x, UE 120 y, etc.) may be dispersed throughoutwireless communications network 100, and each UE may be stationary ormobile. A UE may also be referred to as a mobile station, a terminal, anaccess terminal, a subscriber unit, a station, a Customer PremisesEquipment (CPE), a cellular phone, a smart phone, a personal digitalassistant (PDA), a wireless modem, a wireless communication device, ahandheld device, a laptop computer, a cordless phone, a wireless localloop (WLL) station, a tablet, a camera, a gaming device, a netbook, asmartbook, an ultrabook, a medical device or medical equipment, abiometric sensor/device, a wearable device such as a smart watch, smartclothing, smart glasses, a smart wrist band, smart jewelry (e.g., asmart ring, a smart bracelet, etc.), an entertainment device (e.g., amusic device, a video device, a satellite radio, etc.), a vehicularcomponent or sensor, a smart meter/sensor, industrial manufacturingequipment, a global positioning system device, or any other suitabledevice that is configured to communicate via a wireless or wired medium.Some UEs may be considered evolved or machine-type communication (MTC)devices or evolved MTC (eMTC) devices. MTC and eMTC UEs include, forexample, robots, drones, remote devices, sensors, meters, monitors,location tags, etc., that may communicate with a BS, another device(e.g., remote device), or some other entity. A wireless node mayprovide, for example, connectivity for or to a network (e.g., a widearea network such as Internet or a cellular network) via a wired orwireless communication link. Some UEs may be consideredInternet-of-Things (IoT) devices.

In FIG. 1, a solid line with double arrows indicates desiredtransmissions between a UE and a serving BS, which is a BS designated toserve the UE on the downlink and/or uplink. A finely dashed line withdouble arrows indicates interfering transmissions between a UE and a BS.

Certain wireless networks (e.g., LTE) utilize orthogonal frequencydivision multiplexing (OFDM) on the downlink and single-carrierfrequency division multiplexing (SC-FDM) on the uplink. OFDM and SC-FDMpartition the system bandwidth into multiple (K) orthogonal subcarriers,which are also commonly referred to as tones, bins, etc. Each subcarriermay be modulated with data. In general, modulation symbols are sent inthe frequency domain with OFDM and in the time domain with SC-FDM. Thespacing between adjacent subcarriers may be fixed, and the total numberof subcarriers (K) may be dependent on the system bandwidth. Forexample, the spacing of the subcarriers may be 15 kHz and the minimumresource allocation (called a “resource block” (RB)) may be 12subcarriers (i.e., 180 kHz). Consequently, the nominal Fast FourierTransform (FFT) size may be equal to 128, 256, 512, 1024 or 2048 forsystem bandwidth of 1.25 MHz, 2.5 MHz, 5 MHz, 10 MHz, or 20 MHz,respectively. The system bandwidth may also be partitioned intosubbands. For example, a subband may cover 1.08 MHz (i.e., 6 RBs), andthere may be 1, 2, 4, 8 or 16 subbands for system bandwidth of 1.25 MHz,2.5 MHz, 5 MHz, 10 MHz, or 20 MHz, respectively.

While aspects of the examples described herein may be associated withLTE technologies, aspects of the present disclosure may be applicablewith other wireless communications systems, such as NR.

NR may utilize OFDM with a CP on the uplink and downlink and includesupport for half-duplex operation using TDD. A single component carrierbandwidth of 100 MHz may be supported. NR RBs may span 12 subcarrierswith a subcarrier bandwidth of 75 kHz over a 0.1 ms duration. Each radioframe may consist of 50 subframes with a length of 10 ms. Consequently,each subframe may have a length of 0.2 ms. Each subframe may indicate alink direction (i.e., downlink or uplink) for data transmission and thelink direction for each subframe may be dynamically switched. Eachsubframe may include DL/UL data as well as DL/UL control data. UL and DLsubframes for NR may be as described in more detail below with respectto FIGS. 6 and 7. Beamforming may be supported and beam direction may bedynamically configured. MIMO transmissions with precoding may also besupported. MIMO configurations in the DL may support up to 8 transmitantennas with multi-layer DL transmissions up to 8 streams and up to 2streams per UE. Multi-layer transmissions with up to 2 streams per UEmay be supported. Aggregation of multiple cells may be supported with upto 8 serving cells. Alternatively, NR may support a different airinterface, other than an OFDM-based.

In some examples, access to the air interface may be scheduled. Ascheduling entity (e.g., a BS 110 or UE 120) allocates resources forcommunication among some or all devices and equipment within its servicearea or cell. Within the present disclosure, as discussed further below,the scheduling entity may be responsible for scheduling, assigning,reconfiguring, and releasing resources for one or more subordinateentities. That is, for scheduled communication, subordinate entitiesutilize resources allocated by the scheduling entity. BSs are not theonly entities that may function as a scheduling entity. That is, in someexamples, a UE may function as a scheduling entity, scheduling resourcesfor one or more subordinate entities (e.g., one or more other UEs). Inthis example, the UE is functioning as a scheduling entity, and otherUEs utilize resources scheduled by the UE for wireless communication. AUE may function as a scheduling entity in a peer-to-peer (P2P) network,and/or in a mesh network. In a mesh network example, UEs may optionallycommunicate directly with one another in addition to communicating withthe scheduling entity.

Thus, in a wireless communication network with a scheduled access totime-frequency resources and having a cellular configuration, a P2Pconfiguration, and a mesh configuration, a scheduling entity and one ormore subordinate entities may communicate utilizing the scheduledresources.

The NR radio access network (RAN) may include one or more central units(CU) and distributed units (DUs). A NR BS (e.g., a gNB, a 5G NB, a NB, a5G NB, a TRP, an AP) may correspond to one or multiple BSs. NR cells canbe configured as access cells (ACells) or data only cells (DCells).DCells may be cells used for carrier aggregation or dual connectivity,but not used for initial access, cell selection/reselection, orhandover.

FIG. 2 illustrates an example logical architecture of a distributed RAN200, which may be implemented in wireless communications system 100illustrated in FIG. 1. 5G access node (AN) 206 may include access nodecontroller (ANC) 202. ANC 202 may be a CU of distributed RAN 200. Abackhaul interface to next generation core network (NG-CN) 204 mayterminate at ANC 202. A backhaul interface to neighboring nextgeneration access nodes (NG-ANs) may terminate at ANC 202. ANC 202 mayinclude one or more TRPs 208.

TRPs 208 comprise DUs. TRPs 208 may be connected to one ANC (ANC 202) ormore than one ANC (not illustrated). For example, for RAN sharing, radioas a service (RaaS), and service specific AND deployments, the TRP maybe connected to more than one ANC 202. A TRP 208 may include one or moreantenna ports. TRPs 208 may be configured to individually (e.g., dynamicselection) or jointly (e.g., joint transmission) serve traffic to a UE(e.g., a UE 120).

Example logical architecture of the distributed RAN 200 may be used toillustrate fronthaul definition. The logical architecture may supportfronthauling solutions across different deployment types. For example,the logical architecture may be based on transmit network capabilities(e.g., bandwidth, latency, and/or jitter). The logical architecture mayshare features and/or components with LTE. NG-AN 210 may support dualconnectivity with NR. NG-AN 210 may share a common fronthaul for LTE andNR. The logical architecture may enable cooperation between and amongTRPs 208. For example, cooperation may be pre-configured within a TRP208 and/or across TRPs 208 via ANC 202. There may be no inter-TRPinterface.

The logical architecture for distributed RAN 200 may include a dynamicconfiguration of split logical functions. As will be described in moredetail with reference to FIG. 5, the Radio Resource Control (RRC) layer,Packet Data Convergence Protocol (PDCP) layer, Radio Link Control (RLC)layer, Medium Access Control (MAC) layer, and a Physical (PHY) layersmay be placed at the DU (e.g., a TRP 208) or the CU (e.g., ANC 202).

FIG. 3 illustrates an example physical architecture of a distributed RAN300, according to aspects of the present disclosure. As shown in FIG. 3,distributed RAN 300 includes centralized core network unit (C-CU) 302,centralized RAN unit (C-RU) 304, and DU 306.

C-CU 302 may host core network functions. C-CU 302 may be centrallydeployed. C-CU 302 functionality may be offloaded (e.g., to advancedwireless services (AWS)), in an effort to handle peak capacity. C-RU 304may host one or more ANC functions. Optionally, C-RU 304 may host corenetwork functions locally. C-RU 304 may have a distributed deployment.C-RU 304 may be located near an edge the network. DU 306 may host one ormore TRPs (edge node (EN), an edge unit (EU), a radio head (RH), a smartradio head (SRH), or the like). DU 306 may be located at edges of thenetwork with radio frequency (RF) functionality.

FIG. 4 illustrates example components of the BS 110 and the UE 120illustrated in FIG. 1, which may be used to implement aspects of thepresent disclosure for high performance, flexible, and compact LDPCcoding. One or more of the components of BS 110 and UE 120 illustratedin FIG. 4 may be used to practice aspects of the present disclosure. Forexample, antenna(s) 452 a-454 r, Demodulator(s)/Modulator(s) 454 a-454r, TX MIMO processor 466, Receive Processor 458, Transmit Processor 464,and/or Controller/Processor 480 of UE 120 and/or antenna(s) 434 a 434 t,Demodulator(s)/Modulator(s) 432 a-434 t, TX MIMO Processors 430,Transmit Processor 420, Receive Processor 438, and/orController/Processor 440 of BS 110 may be used to perform the operations1300 described herein and illustrated with reference to FIG. 13.

For a restricted association scenario, BS 110 may be macro BS 110 c inFIG. 1, and UE 120 may be UE 120 y. BS 110 may also be a BS of someother type. BS 110 may be equipped with antennas 434 a through 434 t andUE 120 may be equipped with antennas 452 a through 452 r.

At BS 110, transmit processor 420 may receive data from data source 412and control information from controller/processor 440. The controlinformation may be for the Physical Broadcast Channel (PBCH), PhysicalControl Format Indicator Channel (PCFICH), Physical Hybrid ARQ IndicatorChannel (PHICH), Physical Downlink Control Channel (PDCCH), or othercontrol channel or signal. The data may be for the Physical DownlinkShared Channel (PDSCH), or other data channel or signal. Transmitprocessor 420 may process (e.g., encode and symbol map) the data andcontrol information to obtain data symbols and control symbols,respectively. For example, transmit processor 420 may encode theinformation bits using LPDC code designs discussed in greater detailbelow. Transmit processor 420 may also generate reference symbols, forexample, for the primary synchronization signal (PSS), secondarysynchronization signal (SSS), and cell-specific reference signal (CRS).Transmit (TX) multiple-input multiple-output (MIMO) processor 430 mayperform spatial processing (e.g., precoding) on the data symbols, thecontrol symbols, and/or the reference symbols, if applicable, and mayprovide output symbol streams to the modulators (MODs) 432 a through 432t. Each modulator 432 may process a respective output symbol stream(e.g., for OFDM, etc.) to obtain an output sample stream. Each modulator432 may further process (e.g., convert to analog, amplify, filter, andupconvert) the output sample stream to obtain a downlink signal.Downlink signals from modulators 432 a through 432 t may be transmittedvia antennas 434 a through 434 t, respectively.

At UE 120, antennas 452 a through 452 r may receive the downlink signalsfrom BS 110 and may provide received signals to the demodulators(DEMODs) 454 a through 454 r, respectively. Each demodulator 454 maycondition (e.g., filter, amplify, downconvert, and digitize) arespective received signal to obtain input samples. Each demodulator 454may further process the input samples (e.g., for OFDM, etc.) to obtainreceived symbols. MIMO detector 456 may obtain received symbols from allthe demodulators 454 a through 454 r, perform MIMO detection on thereceived symbols if applicable, and provide detected symbols. Receiveprocessor 458 may process (e.g., demodulate, deinterleave, and decode)the detected symbols, provide decoded data for UE 120 to a data sink460, and provide decoded control information to controller/processor480.

On the uplink, at UE 120, transmit processor 464 may receive and processdata (e.g., for the Physical Uplink Shared Channel (PUSCH) or other datachannel or signal) from data source 462 and control information (e.g.,for the Physical Uplink Control Channel (PUCCH) or other control channelor signal) from controller/processor 480. Transmit processor 464 mayalso generate reference symbols for a reference signal. The symbols fromtransmit processor 464 may be precoded by TX MIMO processor 466 ifapplicable, further processed by demodulators 454 a through 454 r (e.g.,for SC-FDM, etc.), and transmitted to BS 110. At BS 110, the uplinksignals from the UE 120 may be received by antennas 434, processed bymodulators 432, detected by MIMO detector 436 if applicable, and furtherprocessed by receive processor 438 to obtain decoded data and controlinformation sent by UE 120. Receive processor 438 may provide thedecoded data to data sink 439 and the decoded control information tocontroller/processor 440.

Memory 442 may store data and program codes for BS 110 and memory 482may store data and program codes for UE 120. Scheduler 444 may scheduleUEs for data transmission on the downlink and/or uplink.

FIG. 5 illustrates a diagram 500 showing examples for implementing acommunications protocol stack, according to aspects of the presentdisclosure. The illustrated communications protocol stacks may beimplemented by devices operating in a in a 5G system (e.g., a systemthat supports uplink-based mobility). Diagram 500 illustrates acommunications protocol stack including RRC layer 510, PDCP layer 515,RLC layer 520, MAC layer 525, and PHY layer 530. In an example, thelayers of a protocol stack may be implemented as separate modules ofsoftware, portions of a processor or ASIC, portions of non-collocateddevices connected by a communications link, or various combinationsthereof. Collocated and non-collocated implementations may be used, forexample, in a protocol stack for a network access device (e.g., ANs,CUs, and/or DUs) or a UE.

A first option 505-a shows a split implementation of a protocol stack,in which implementation of the protocol stack is split between acentralized network access device (e.g., ANC 202) and distributednetwork access device (e.g., DU 208). In the first option 505-a, RRClayer 510 and PDCP layer 515 may be implemented by the CU, and RLC layer520, MAC layer 525, and PHY layer 530 may be implemented by the DU. Invarious examples, the CU and the DU may be collocated or non-collocated.The first option 505-a may be useful in a macro cell, micro cell, orpico cell deployment.

A second option 505-b shows a unified implementation of a protocolstack, in which the protocol stack is implemented in a single networkaccess device (e.g., access node (AN), NR BS, a NR NB, a network node(NN), TRP, gNB, etc.). In the second option, RRC layer 510, PDCP layer515, RLC layer 520, MAC layer 525, and PHY layer 530 may each beimplemented by the AN. The second option 505-b may be useful in a femtocell deployment.

Regardless of whether a network access device implements part or all ofa protocol stack, a UE may implement the entire protocol stack (e.g.,RRC layer 510, PDCP layer 515, RLC layer 520, MAC layer 525, and PHYlayer 530).

FIG. 6 is a diagram showing an example of a DL-centric subframe 600. TheDL-centric subframe 600 may include control portion 602. Control portion602 may exist in the initial or beginning portion of DL-centric subframe600. Control portion 602 may include various scheduling informationand/or control information corresponding to various portions ofDL-centric subframe 600. In some configurations, control portion 602 maybe a physical DL control channel (PDCCH), as shown in FIG. 6. DL-centricsubframe 600 may also include DL data portion 604. DL data portion 604may be referred to as the payload of DL-centric subframe 600. DL dataportion 604 may include the communication resources utilized tocommunicate DL data from the scheduling entity (e.g., UE or BS) to thesubordinate entity (e.g., UE). In some configurations, DL data portion604 may be a physical DL shared channel (PDSCH).

DL-centric subframe 600 may also include common UL portion 606. CommonUL portion 606 may be referred to as an UL burst, a common UL burst,and/or various other suitable terms. Common UL portion 606 may includefeedback information corresponding to various other portions ofDL-centric subframe 600. For example, common UL portion 606 may includefeedback information corresponding to control portion 602. Non-limitingexamples of feedback information may include an acknowledgment (ACK)signal, a negative acknowledgment (NACK) signal, a HARQ indicator,and/or various other suitable types of information. Common UL portion606 may additionally or alternatively include information, such asinformation pertaining to random access channel (RACH) procedures,scheduling requests (SRs), and various other suitable types ofinformation. As illustrated in FIG. 6, the end of DL data portion 604may be separated in time from the beginning of common UL portion 606.This time separation may be referred to as a gap, a guard period, aguard interval, and/or various other suitable terms. This separationprovides time for the switch-over from DL communication (e.g., receptionoperation by the subordinate entity (e.g., UE)) to UL communication(e.g., transmission by the subordinate entity (e.g., UE)). The foregoingis merely one example of a DL-centric subframe and alternativestructures having similar features may exist without necessarilydeviating from the aspects described herein.

FIG. 7 is a diagram showing an example of an UL-centric subframe 700.UL-centric subframe 700 may include control portion 702. Control portion702 may exist in the initial or beginning portion of UL-centric subframe700. Control portion 702 in FIG. 7 may be similar to control portion 602described above with reference to FIG. 6. UL-centric subframe 700 mayalso include UL data portion 704. UL data portion 704 may be referred toas the payload of UL-centric subframe 700. UL data portion 704 may referto the communication resources utilized to communicate UL data from thesubordinate entity (e.g., UE) to the scheduling entity (e.g., UE or BS).In some configurations, control portion 702 may be a PDCCH.

As illustrated in FIG. 7, the end of control portion 702 may beseparated in time from the beginning of UL data portion 704. This timeseparation may be referred to as a gap, guard period, guard interval,and/or various other suitable terms. This separation provides time forthe switch-over from DL communication (e.g., reception operation by thescheduling entity) to UL communication (e.g., transmission by thescheduling entity). UL-centric subframe 700 may also include common ULportion 706. Common UL portion 706 in FIG. 7 may be similar to thecommon UL portion 606 described above with reference to FIG. 6. CommonUL portion 706 may additionally or alternatively include informationpertaining to channel quality indicator (CQI), sounding referencesignals (SRSs), and various other suitable types of information. Theforegoing is merely one example of an UL-centric subframe andalternative structures having similar features may exist withoutnecessarily deviating from the aspects described herein.

In some circumstances, two or more subordinate entities (e.g., UEs) maycommunicate with each other using sidelink signals. Real-worldapplications of such sidelink communications may include public safety,proximity services, UE-to-network relaying, vehicle-to-vehicle (V2V)communications, Internet-of-Everything (IoE) communications, IoTcommunications, mission-critical mesh, and/or various other suitableapplications. Generally, a sidelink signal may refer to a signalcommunicated from one subordinate entity (e.g., UE1) to anothersubordinate entity (e.g., UE2) without relaying that communicationthrough the scheduling entity (e.g., UE or BS), even though thescheduling entity may be utilized for scheduling and/or controlpurposes. In some examples, the sidelink signals may be communicatedusing a licensed spectrum (unlike wireless local area networks (WLAN),which typically use an unlicensed spectrum).

A UE may operate in various radio resource configurations, including aconfiguration associated with transmitting pilots using a dedicated setof resources (e.g., a radio resource control (RRC) dedicated state,etc.) or a configuration associated with transmitting pilots using acommon set of resources (e.g., an RRC common state, etc.). Whenoperating in the RRC dedicated state, the UE may select a dedicated setof resources for transmitting a pilot signal to a network. Whenoperating in the RRC common state, the UE may select a common set ofresources for transmitting a pilot signal to the network. In eithercase, a pilot signal transmitted by the UE may be received by one ormore network access devices, such as an AN, or a DU, or portionsthereof. Each receiving network access device may be configured toreceive and measure pilot signals transmitted on the common set ofresources, and also receive and measure pilot signals transmitted ondedicated sets of resources allocated to the UEs for which the networkaccess device is a member of a monitoring set of network access devicesfor the UE. One or more of the receiving network access devices, or a CUto which receiving network access device(s) transmit the measurements ofthe pilot signals, may use the measurements to identify serving cellsfor the UEs, or to initiate a change of serving cell for one or more ofthe UEs.

Example Error Correction Coding Features

Many communications systems use error-correcting codes. Specifically,error correcting codes compensate for the intrinsic unreliability ofinformation transfer in these systems by introducing redundancy into thedata stream. Low-density parity-check (LDPC) codes are a particular typeof error correcting codes which use an iterative coding system. Gallagercodes are an early example of “regular” LDPC codes. Regular LDPC codesare linear block code in which most of the elements of its parity checkmatrix H are ‘0’.

LDPC codes can be represented by bipartite graphs (often referred to as“Tanner graphs”). In the bipartite graph, a set of variable nodescorresponds to bits of a codeword (e.g., information bits or systematicbits) and a set of check nodes correspond to a set of parity-checkconstraints that define the code. Thus, the nodes of the graph areseparated into two distinctive sets and with edges connecting nodes oftwo different types, variable and check. A regular graph or code is onefor which all variable nodes have the same degree and all constraintnodes have the same degree. In this case, the code is a regular code. Onthe other hand, an irregular code has constraint nodes and/or variablenodes of differing degrees. For example, some variable nodes may be ofdegree 4, others of degree 3 and still others of degree 2.

“Lifting” enables LDPC codes to be implemented using parallel encodingand/or decoding implementations while also reducing the complexitytypically associated with large LDPC codes. More specifically, liftingis a technique for generating a relatively large LDPC code from multiplecopies of a smaller base code. For example, a lifted LDPC code may begenerated by producing a number (Z) of parallel copies of the base graphand then interconnecting the parallel copies through permutations ofedge clusters of each copy of the base graph. Thus, a larger graph canbe obtained by a “copy and permute” operation where multiple copies areoverlaid so that same-type vertices are in close proximity, but theoverall graph consists of multiple disconnected subgraphs.

A lifted graph is created by copying a bipartite base graph (G), whichmay also be referred to as the protograph, a number of times, Z whichmay be referred to as the lifting, lifting size, or lifting size value.A variable node and a check node are considered “neighbors” if they areconnected by an “edge” (i.e., the line connecting the variable node andthe check node) in the graph. In addition, for each edge (e) of thebipartite base graph (G), a permutation is applied to the Z copies ofedge (e) to interconnect the N copies of G. The permutation is generallyan integer value k associated with the edge, which may be referred to asthe lifting value. A bit sequence having a one-to-one association withthe variable node sequence is a valid codeword if and only if, for eachcheck node, the bits associated with all neighboring variable nodes sumto zero modulo two (i.e., they include an even number of 1's). Theresulting LDPC code may be quasi-cyclic (QC) if the permutations(lifting values) used are cyclic.

FIGS. 8-8A show graphical and matrix representations, respectively, ofan example LDPC code, in accordance with certain aspects of the presentdisclosure. For example, FIG. 8 shows a bipartite graph 800 representingthe LDPC code. The bipartite graph 800 includes a set of 5 variablenodes 810 (represented by circles) connected to 4 check nodes 820(represented by squares). Edges in the bipartite graph 800 connectvariable nodes 810 to the check nodes 820 (represented by the linesconnecting the variable nodes 810 to the check nodes 820). Thus, thebipartite graph 800 consists of V=5 variable nodes and C=4 check nodes,connected by E=12 edges.

The bipartite graph 800 may be represented by a simplified adjacencymatrix, as shown in FIG. 8A. The matrix representation 800A includes aparity check matrix (PCM) H and a codeword vector x, where x₁-x₅represent bits of the codeword x. H is used to determine if a receivedsignal was normally decoded. H has C rows corresponding to j check nodesand V columns corresponding to i variable nodes (i.e., a demodulatedsymbol), where the rows represent the equations and the columnsrepresents the bits of the codeword. In FIG. 8A, H has 4 rows and 5columns corresponding to 4 check nodes and 5 variable nodes from thebipartite graph 800, respectively. If a j-th check node is connected toan i-th variable node by an edge (i.e., the two nodes are neighbors),then there is a “1” in the i-th column and in the j-th row of H. Thatis, the intersection of an i-th row and a j-th column contains a “1”where an edge joins the corresponding vertices and a “0” where there isno edge. The codeword vector x represents a valid codeword if and onlyif H_(x)=0 (e.g., if, for each constraint node, the bits neighboring theconstraint (via their association with variable nodes) sum to 0 modulo 2(i.e., they comprise an even number of ones). Thus, if the codeword isreceived correctly, then H_(x)=0 (mod 2). When the product of a codedreceived signal and H becomes “0”, this signifies that no error hasoccurred.

The number of demodulated symbols or variable nodes is the LDPC codelength. The number of non-zero elements in a row (column) is defined asthe row (column) weight d(c)d(v). The degree of a node refers to thenumber of edges connected to that node. For example, as shown in FIG. 8,the variable node 801 has three degrees of connectivity, with edgesconnected to check nodes 811, 812, and 813. Variable node 802 has threedegrees of connectivity, with edges connected to check nodes 811, 813,and 814. Variable node 803 has two degrees of connectivity, with edgesconnected to check nodes 811 and 814. Variable node 804 has two degreesof connectivity, with edges connected to check nodes 812 and 814. Andvariable node 805 has two degrees of connectivity, with edges connectedto check nodes 812 and 813. This feature is illustrated in the matrix Hshown in FIG. 8A where the number of edges incident to a variable node810 is equal to the number of 1's in the corresponding column and iscalled the variable node degree d(v). Similarly, the number of edgesconnected with a check node 820 is equal to the number of 1's in acorresponding row and is called the check node degree d(c). For example,as shown in FIG. 8A, the first column in the matrix H corresponds to thevariable node 801 and the corresponding entries in the column (1, 1, 1,0) indicates the edge connections to the check nodes 811, 812, and 813,while the 0 indicates that there is not an edge to check node 814. Theentries in the second, third, fourth, and fourth columns of H representthe edge connections of the variable nodes 802, 803, 804, and 805,respectively, to the check nodes.

FIG. 9 is a bipartite graph 900 illustrating the liftings of threecopies of the bipartite graph 800 of FIG. 8. Three copies may beinterconnected by permuting like edges among the copies. If thepermutations are restricted to cyclic permutations, then the resultinggraph corresponds to a quasi-cyclic LDPC with lifting Z=3. The originalgraph from which three copies were made is referred to herein as thebase graph. To derive graphs of different sizes from the base graph, a“copy and permute” operation can be applied to the base graph.

A corresponding PCM of the lifted graph can be constructed from the PCMof the base graph by replacing each entry in the base PCM with a Z×Zmatrix. The “0” entries (those having no base edges) are replaced withthe 0 matrix and the 1 entries (indicating a base edge) are replacedwith a Z x Z permutation matrix. In the case of cyclic liftings, thepermutations are cyclic permutations.

A cyclically lifted LDPC code can also be interpreted as a code over thering of binary polynomials modulo x^(z)+1. In this interpretation, abinary polynomial, (x)=b₀+b₁x+b₂x² +. . . +b_(z-1)x^(z-1) may beassociated to each variable node in the base graph. The binary vector(b₀, b₁, b₂, . . . , b_(z-1)) corresponds to the bits associated to Zcorresponding variable nodes in the lifted graph, that is, Z copies of asingle base variable node. A cyclic permutation by k (referred to as alifting value associated to the edges in the graph) of the binary vectoris achieved by multiplying the corresponding binary polynomial by x^(k)where multiplication is taken modulo x^(z)+1. A degree d parity check inthe base graph can be interpreted as a linear constraint on theneighboring binary polynomials B₁(x), . . . , B_(d)(x), written as x^(k)¹ B₁(x)+x^(k) ² B₂(x)+ . . . +x^(k) ^(d) B_(d)(x)=0x^(k) ¹ B₁(x)+x^(k) ²B₂(x)+ . . . +x^(k) ^(d) B_(d)(x)=0, the values, k₁, . . . , k_(d) arethe cyclic lifting values associated to the corresponding edges.

This resulting equation is equivalent to the Z parity checks in thecyclically lifted Tanner graph corresponding to the single associatedparity check in the base graph. Thus, the parity check matrix for thelifted graph can be expressed using the matrix for the base graph inwhich 1 entries are replaced with monomials of the form x^(k) and 0entries are lifted as 0, but now the 0 is interpreted as the 0 binarypolynomial modulo x^(z)+1. Such a matrix may be written by giving thevalue k in place of x^(k). In this case the 0 polynomial is sometimesrepresented as “−1” and sometimes as another character in order todistinguish it from x⁰.

Typically, a square submatrix of the parity check matrix represents theparity bits of the code. The complementary columns correspond toinformation bits that, at the time of encoding, are set equal to theinformation bits to be encoded. The encoding may be achieved by solvingfor the variables in the aforementioned square submatrix in order tosatisfy the parity check equations. The matrix H may be partitioned intotwo parts M and N where M is the square portion. Thus, encoding reducesto solving M_(c)=s=Nd where c and d comprise x. In the case ofquasi-cyclic codes, or cyclically lifted codes, the above algebra can beinterpreted as being over the ring of binary polynomials modulo x^(z)+1.In the case of the 802.11 LDPC codes, which are quasi-cyclic, theencoding submatrix M has an integer representation as shown in FIG. 10.

A received LDPC codeword can be decoded to produce a reconstructedversion of the original codeword. In the absence of errors, or in thecase of correctable errors, decoding can be used to recover the originaldata unit that was encoded. Redundant bits may be used by decoders todetect and correct bit errors. LDPC decoder(s) generally operate byiteratively performing local calculations and passing those results byexchanging messages within the bipartite graph 800, along the edges, andupdating these messages by performing computations at the nodes based onthe incoming messages. These steps may typically be repeated severaltimes. For example, each variable node 810 in the graph 800 mayinitially be provided with a “soft bit” (e.g., representing the receivedbit of the code word) that indicates an estimate of the associated bit'svalue as determined by observations from the communications channel.Using these soft bits the LDPC decoders may update messages byiteratively reading them, or some portion thereof, from memory andwriting an updated message, or some portion thereof, back to, memory.The update operations are typically based on the parity checkconstraints of the corresponding LDPC code. In implementations forlifted LDPC codes, messages on like edges are often processed inparallel.

LDPC codes designed for high-speed applications often use quasi-cyclicconstructions with large lifting factors and relatively small basegraphs to support high parallelism in encoding and decoding operations.LDPC codes with higher code rates (e.g., the ratio of the message lengthto the codeword length) tend to have relatively fewer parity checks. Ifthe number of base parity checks is smaller than the degree of avariable node (e.g., the number of edges connected to a variable node),then, in the base graph, that variable node is connected to at least oneof the base parity checks by two or more edges (e.g., the variable nodemay have a “double edge”). If the number of base parity checks issmaller than the degree of a variable node (e.g., the number of edgesconnected to a variable node), then, in the base graph, that variablenode is connected to at least one of the base parity checks by two ormore edges. Having a base variable node and a base check node connectedby two or more edges is generally undesirable for parallel hardwareimplementation purposes. For example, such double edges may result inmultiple concurrent read and write operations to the same memorylocations, which in turn may create data coherency problems. A doubleedge in a base LDPC code may trigger parallel reading of the same softbit value memory location twice during a single parallel parity checkupdate. Thus, additional circuitry is typically needed to combine thesoft, bit values that are written back to memory, so as to properlyincorporate both updates. Eliminating double edges in the LDPC codehelps to avoid this extra complexity

LDPC code designs based on cyclic lifting can be interpreted as codesover the ring of polynomials modulo may be binary polynomials modulox^(z)−1, where Z is the lifting size (e.g., the size of the cycle in thequasi-cyclic code). Thus, encoding such codes can often be interpretedas an algebraic operation in this ring.

In the definition of standard irregular LDPC code ensembles (degreedistributions) all edges in the Tanner graph representation may bestatistically interchangeable. In other words, there exists a singlestatistical equivalence class of edges. For multi-edge LDPC codes,multiple equivalence classes of edges may be possible. While in thestandard irregular LDPC ensemble definition, nodes in the graph (bothvariable and constraint) are specified by their degree, i.e., the numberof edges they are connected to, in the multi-edge type setting an edgedegree is a vector; it specifies the number of edges connected to thenode from each edge equivalence class (type) independently. A multi-edgetype ensemble is comprised of a finite number of edge types. The degreetype of a constraint node is a vector of (non-negative) integers; thei-th entry of this vector records the number of sockets of the i-th typeconnected to such a node. This vector may be referred to as an edgedegree. The degree type of a variable node has two parts although it canbe viewed as a vector of (non-negative) integers. The first part relatesto the received distribution and will be termed the received degree andthe second part specifies the edge degree. The edge degree plays thesame role as for constraint nodes. Edges are typed as they pair socketsof the same type. The constraint, that sockets must pair with sockets oflike type, characterizes the multi-edge type concept. In a multi-edgetype description, different node types can have different receiveddistributions (e.g., the associated bits may go through differentchannels).

Puncturing is performed by removing bits from a codeword to generate ashorter codeword. Thus, punctured variable nodes correspond to codewordbits that are not actually transmitted. Puncturing a variable node in anLDPC code creates a shortened code (e.g., due to the removal of a bit),while also effectively removing a check node. Specifically, for a matrixrepresentation of an LDPC code, including bits to be punctured, wherethe variable node to be punctured has a degree of one (e.g., by rowcombining), puncturing the variable node removes the associated bit fromthe code and effectively removes its single neighboring check node fromthe graph. As a result, the number of check nodes in the graph isreduced by one. Puncturing can be performed according to puncturingpattern. The puncturing pattern specifies the bits to be punctured.

FIG. 11 is a simplified block diagram illustrating an encoder, inaccordance with certain aspects of the present disclosure. FIG. 11 is asimplified block diagram 1100 illustrating a portion of a radiofrequency (RF) modem 1150 that may be configured to provide a signalincluding an encoded message for wireless transmission. In one example,a convolutional encoder 1102 in a BS 110 (or a UE 120 on the reversepath) receives a message 1120 for transmission. The message 1120 maycontain data and/or encoded voice or other content directed to thereceiving device. The encoder 1102 encodes the message using a suitablemodulation and coding scheme (MCS), typically selected based on aconfiguration defined by the BS 110 or another network entity. Anencoded bitstream 1122 produced by the encoder 1102 may then beselectively punctured by a puncturing module 1104, which may be aseparate device or component, or which may be integrated with theencoder 1102. The puncturing module 1104 may determine that thebitstream should be punctured prior to transmission, or transmittedwithout puncturing. The decision to puncture the bitstream 1122 istypically made based on network conditions, network configuration, RANdefined preferences and/or for other reasons. The bitstream 1122 may bepunctured according to a puncture pattern 1112 and used to encode themessage 1120. The puncturing module 1104 provides an output 1124 to amapper 1106 that generates a sequence of Tx symbols 1126 that aremodulated, amplified, and otherwise processed by Tx chain 1108 toproduce an RF signal 1128 for transmission through antenna 1110.

The output 1124 of the puncturing module 1104 may be the unpuncturedbitstream 1122 or a punctured version of the bitstream 1122, accordingto whether the modem portion 1150 is configured to puncture thebitstream 1122. In one example, parity and/or other error correctionbits may be punctured in the output 1124 of the encoder 1102 in order totransmit the message 1120 within a limited bandwidth of the RF channel.In another example, the bitstream may be punctured to reduce the powerneeded to transmit the message 1120, to avoid interference, or for othernetwork-related reasons. These punctured codeword bits are nottransmitted.

The decoders and decoding algorithms used to decode LDPC codewordsoperate by exchanging messages within the graph along the edges andupdating these messages by performing computations at the nodes based onthe incoming messages. Each variable node in the graph is initiallyprovided with a soft bit, termed a received value, that indicates anestimate of the associated bit's value as determined by observationsfrom, for example, the communications channel. Ideally, the estimatesfor separate bits are statistically independent. This ideal may beviolated in practice. A received word is comprised of a collection ofreceived values.

FIG. 12 is a simplified block diagram illustrating a decoder, inaccordance with certain aspects of the present disclosure. FIG. 12 is asimplified schematic 1200 illustrating a portion of a RF modem 1250 thatmay be configured to receive and decode a wirelessly transmitted signalincluding a punctured encoded message. The punctured codeword bits maybe treated as erased. For example, the LLRs of the punctured nodes maybe set to “0” at initialization. In various examples, the modem 1250receiving the signal may reside at the UE, at the BS, or at any othersuitable apparatus or means for carrying out the described functions. Anantenna 1202 provides an RF signal 1220 to a UE. An RF chain 1204processes and demodulates the RF signal 1220 and may provide a sequenceof symbols 1222 to a demapper 1206, which produces a bitstream 1224representative of the encoded message.

The demapper 1206 may provide a depunctured bitstream 1224. In oneexample, the demapper 1206 may include a depuncturing module that can beconfigured to insert null values at locations in the bitstream at whichpunctured bits were deleted by the transmitter. The depuncturing modulemay be used when the puncture pattern 1210 used to produce the puncturedbitstream at the transmitter is known. The puncture pattern 1210 can beused to identify LLRs 1228 that may be ignored during decoding of thebitstream 1224 by the convolutional decoder 1208. The LLRs may beassociated with a set of depunctured bit locations in the bitstream1224. Accordingly, the decoder 1208 may produce the decoded message 1226with reduced processing overhead by ignoring the identified LLRs 1228.The LDPC decoder may include a plurality of processing elements toperform the parity check or variable node operations in parallel. Forexample, when processing a codeword with lifting size Z, the LDPCdecoder may utilize a number (Z) of processing elements to performparity check operations on all Z edges of a lifted graph, concurrently.

Processing efficiency of a decoder 1208 may be improved by configuringthe decoder 1208 to ignore LLRs 1228 that correspond to punctured bitsin a message transmitted in a punctured bitstream 1222. The puncturedbitstream 1222 may have been punctured according to a puncturing schemethat defines certain bits to be removed from an encoded message. In oneexample, certain parity or other error-correction bits may be removed. Apuncturing pattern may be expressed in a puncturing matrix or table thatidentifies the location of bits to be punctured in each message. Apuncturing scheme may be selected to reduce processing overhead used todecode the message 1226 while maintaining compliance with data rates onthe communication channel and/or with transmission power limitations setby the network. A resultant punctured bitstream typically exhibits theerror-correcting characteristics of a high rate error-correction code,but with less redundancy. Accordingly, puncturing may be effectivelyemployed to reduce processing overhead at the decoder 1208 in thereceiver when channel conditions produce a relatively high signal tonoise ratio (SNR).

A convolutional decoder 1208 may be used to decode m-bit informationstrings from a bitstream that has been encoded using a convolutionalcode. The decoder 1208 may comprise a Viterbi decoder, an algebraicdecoder, or another suitable decoder. In one example, a Viterbi decoderemploys the well-known Viterbi algorithm to find the most likelysequence of signaling states (the Viterbi path) that corresponds to areceived bitstream 1224. The bitstream 1224 may be decoded based on astatistical analysis of LLRs calculated for the bitstream 1224. In oneexample, a Viterbi decoder may compare and select the correct Viterbipath that defines a sequence of signaling states using a likelihoodratio test to generate LLRs from the bitstream 1224. Likelihood ratioscan be used to statistically compare the fit of a plurality of candidateViterbi paths using a likelihood ratio test that compares the logarithmof a likelihood ratio for each candidate Viterbi path (i.e. the LLR) todetermine which path is more likely to account for the sequence ofsymbols that produced the bitstream 1224.

At the receiver, the same decoder used for decoding non-puncturedbitstreams can typically be used for decoding punctured bitstreams,regardless of how many bits have been punctured. In conventionalreceivers, the LLR information is typically de-punctured before decodingis attempted by filling LLRs for punctured states or positions(de-punctured LLRs) with zeros. A decoder may disregard de-puncturedLLRs that effectively carry no information.

Example Enhanced Puncturing and LDPC Code Structure Features

One of the desirable properties for low-density parity-check (LDPC)codes intended for wireless transmission is high performance for bothGaussian noise channels and fading channels. It is also desirable thatthe maximum degree of variable nodes (e.g., the degree of connectivity,or number of connections, of the variable nodes in the graph to thecheck nodes in the graph) is not very large (e.g., relative to areference LDPC code).

Certain systems (e.g., 802.11n, 802.11ad, WiMAX, ATSC, etc.) may use amulti-edge type LDPC code structure. Multi-edge type LDPC codes may haveadvantages over the standard irregular LDPC codes. For example, themulti-edge type LDPC code structure may provide many more degrees offreedom than the standard irregular LDPC codes, which can be exploitedto design codes with excellent performance, low encoding/decodingcomplexity, and/or other desirable properties.

Multi-edge type constructions can introduce high-degree puncturedvariable nodes into the design so that the gap to capacity can bereduced with bounded node degrees. Although punctured nodes help toachieve the design goal known as the matching condition, punctured nodescan cause the iterative decoder to slow down at the beginning of thedecoding process. For example, the punctured nodes send out erasureinformation along outgoing edges causing the connected check nodes tosend out little or no information in the first few iterations. In thecontext of lifted LDPC codes, for a code constructed by lifting (e.g.,copying) a relatively small base code, it is often desirable that thebase code have no or few double edges (e.g., a variable node connectedto a check node by two edges). Because high degree variable nodes areconnected to many check nodes, high degree variable nodes may lead tocreation of double edges, for example, at higher rates when the numberof check nodes is relatively small.

Another desirable property for LDPC codes is support for hybridautomatic repeat request (HARQ) extensions. HARQ extensions can involveadding additional parity bits and splitting pre-existing parity checkswith the addition of a one-degree variable node. If both halves of thesplit are connected to a punctured variable node, which may be desirablein order to achieve desired performance, then the pre-split check nodemay have at least two edges that are connected to punctured variablenodes. For example, LDPC code designs with a single high-degreepunctured variable node the presence of double edges in the base code.Thus, it may be desirable to have multiple punctured variable nodes ofsmaller degree rather than one punctured variable node of large degree;however, for high rate codes it may be difficult to achieve goodperformance. In other words, there may be a tradeoff between avoidingdouble edges and achieving higher code rates.

Accordingly, techniques for puncturing of LDPC codes having few doubleedges but still able to achieve high performance over a wide range coderates are desirable.

Techniques are provided herein for enhanced puncturing of multiplevariables nodes of the highest degree in the base graph, but ofrelatively low degree variable nodes relative to other types of LPDCcodes, and LDPC code structures having additional parity bits added tothe multi-edge type LDPC code structure that may help achieve a desiredcode rate and performance over Gaussian and fading channels.

FIG. 13 illustrates example operations 1300 for wireless communication,in accordance with certain aspects of the present disclosure. Operations1300 may be performed, for example, by a transmitting device (e.g., UE120 or BS 110). Operations 1300 may begin, at 1302, by encoding a set ofinformation bits based on a LDPC code (e.g., a multi-edge type LDPCcode) to produce a code word. The LDPC code is defined by a base matrixhaving a first number of variable nodes (columns in the base matrix) anda second number of check nodes (rows in the base matrix). The variablenodes may have a low degree of connectivity to the check nodes relativeto variable nodes in a reference LDPC code (e.g., an LDPC code having asingle high-degree punctured node) and the base matrix has at least oneadditional parity bit (e.g., M−1 extra variable nodes or one extravariable node for each pair of punctured variable nodes) for thepunctured variable nodes. At 1304, the transmitting device punctures thecode word according to a puncturing pattern designed to puncture bitscorresponding to at least two (e.g., M variable nodes) of the variablenodes (e.g., the two highest-degree variable nodes of the base matrix)to produce a punctured code word. At 1306, the transmitting device addsat least additional parity bit to the base graph for at least one pairof the at least two punctured variable nodes.

At 1308, the transmitting device transmits the punctured code word.According to certain aspects, the at least one extra variable node isformed by a parity of two punctured variable nodes. The at least oneextra variable nodes may have a degree of connectivity to the checknodes of one.

According to certain aspects, an LDPC code can be designed havingmultiple lower degree nodes punctured instead of puncturing a singlehigh-degree node. For example, two nodes of a certain degree may bepunctured instead of one punctured node of twice the degree. Thepunctured variable nodes may be the highest degree variable nodes in theLDPC code structure, but still relatively low-degree variable nodesrelative to other (e.g., conventional) LDPC codes with a singlehigh-degree punctured variable node. The presence of two punctured nodesthat are lower degree nodes may contribute to slower decodingconvergence for those nodes, which may make it more difficult to achievegood performance for high rate codes, particularly, where the number ofcheck nodes is relatively small. In some cases, the punctured nodes maybe the highest degree nodes in the base graph (i.e., the variables nodeshaving the most connected edges to check nodes in the base graph);however, the punctured nodes may have a low degree of connectivityrelative to a highest possible degree of connectivity or degree ofpunctured nodes in a reference LDPC code.

According to certain aspects, additional non-punctured bit(s) may beadded to the LDPC code structure. The additional non-punctured bits maybe formed by taking the parity of the two punctured nodes (e.g., theparity bits may be one degree variable nodes). Adding the extranon-punctured bits to the LDPC code structure may have the effect ofreducing the net puncturing rate. The overall structure of two puncturednodes and one additional transmitted parity bit effectively puncturesonly one degree of freedom from the code. The punctured nodes remain sothat their benefits are still present, but the parity bit may allow morerapid convergence and, thereby, facilitate the determination of thepunctured bits' values in the decoding process. This structure may helpimprove the performance of the overall design on both Gaussian andfading channels while providing support for the other desirable featuresdiscussed above.

According to certain aspects, LDPC code structures may be used in whichthe base graph has some small number of punctured variable nodes ofmoderate (e.g., relatively low) degree (e.g., degree 3 to degree 7). TheLDPC code structure may also contain additional parity bit(s) eachformed from two such punctured nodes.

In one example implementation, an LDPC code structure having a basegraph of length 27 or 28 may be used. In the base graph, two low degreevariable nodes may be punctured and one additional parity bit may beadded to the LDPC code structure, formed by a parity of the twopunctured nodes. This LDPC code structure may useful, for example, forcode rates of one-fourth to eight-ninths.

According to certain aspects, LDPC code structures having a large basegraph may involve larger number of punctured low degree nodes and alarger number of associated parity bits added. For example, for mpunctured variable nodes, m−1 one degree parity bits may be added.Although in other cases a different number of parity bits may be added,for example, in some cases few than m−1 parity bits may be used. Inanother example implementation illustrated in FIG. 14, an LDPC codestructure 1400 having a base graph of length 36 may be used. In the basegraph, the three highest degree variable nodes 1304 in the LDPC codestructure 1400, having a relatively low-degree, are punctured and twoadditional parity bits 1306 are added to the LDPC code structure 1400,each formed by a parity of two of the punctured nodes and are connectedto one of the check nodes 1402.

It may be noted that the degree of the relatively low degree puncturednodes does not include edges used to form the additional parity bits. InHARQ extensions, the degrees of the punctured nodes may increasesubstantially due to the addition of further parity bits. One of theadvantages of the multi-edge type designs is that they allow theintroduction of degree one variable nodes in a controlled manner. Bypuncturing all degree one variable nodes and stripping those variablenodes off of the code graph by removing their associated check node aswell, a “core” graph may be obtained. The “degree” of the puncturedvariable nodes may be the degree of the nodes in the core graph.

The techniques and apparatus described herein for generating LDPC codestructure having at least two punctured, relatively low degree variablenodes, and adding additional parity bits for the punctured pairs ofvariable nodes may provide better encoder/decoder operations and, thus,enhanced performance of a processor and/or processing systems. Forexample, use of lower punctured nodes helps avoid the presence of doubleedge in the graph that can slow iterative decoding. By adding theadditional parity bits to the base graph for the punctured variablenodes, good performance can be still obtained, even in the presence ofthe punctured variable nodes, and higher code rates can be achievedwhile still avoiding creation of double edges in the graph. Thus,encoding/decoding using the proposed LDPC code structures leads toimproved processing times.

The methods disclosed herein comprise one or more steps or actions forachieving the described method. The method steps and/or actions may beinterchanged with one another without departing from the scope of theclaims. In other words, unless a specific order of steps or actions isspecified, the order and/or use of specific steps and/or actions may bemodified without departing from the scope of the claims.

As used herein, the term “determining” encompasses a wide variety ofactions. For example, “determining” may include calculating, computing,processing, deriving, investigating, looking up (e.g., looking up in atable, a database or another data structure), ascertaining and the like.Also, “determining” may include receiving (e.g., receiving information),accessing (e.g., accessing data in a memory) and the like. Also,“determining” may include resolving, selecting, choosing, establishingand the like.

In some cases, rather than actually transmitting a frame, a device mayhave an interface to output a frame for transmission. For example, aprocessor may output a frame, via a bus interface, to an RF front endfor transmission. Similarly, rather than actually receiving a frame, adevice may have an interface to obtain a frame received from anotherdevice. For example, a processor may obtain (or receive) a frame, via abus interface, from an RF front end for transmission.

The various operations of methods described above may be performed byany suitable means capable of performing the corresponding functions.The means may include various hardware and/or software component(s)and/or module(s), including, but not limited to a circuit, anapplication specific integrated circuit (ASIC), or processor. Generally,where there are operations illustrated in figures, those operations mayhave corresponding counterpart means-plus-function components withsimilar numbering.

The various illustrative logical blocks, modules and circuits describedin connection with the present disclosure may be implemented orperformed with a general purpose processor, a digital signal processor(DSP), an application specific integrated circuit (ASIC), a fieldprogrammable gate array (FPGA) or other programmable logic device (PLD),discrete gate or transistor logic, discrete hardware components, or anycombination thereof designed to perform the functions described herein.A general-purpose processor may be a microprocessor, but in thealternative, the processor may be any commercially available processor,controller, microcontroller, or state machine. A processor may also beimplemented as a combination of computing devices, e.g., a combinationof a DSP and a microprocessor, a plurality of microprocessors, one ormore microprocessors in conjunction with a DSP core, or any other suchconfiguration.

If implemented in hardware, an example hardware configuration maycomprise a processing system in a wireless node. The processing systemmay be implemented with a bus architecture. The bus may include anynumber of interconnecting buses and bridges depending on the specificapplication of the processing system and the overall design constraints.The bus may link together various circuits including a processor,machine-readable media, and a bus interface. The bus interface may beused to connect a network adapter, among other things, to the processingsystem via the bus. The network adapter may be used to implement thesignal processing functions of the PHY layer. In the case of a wirelessnode (see FIG. 1), a user interface (e.g., keypad, display, mouse,joystick, etc.) may also be connected to the bus. The bus may also linkvarious other circuits such as timing sources, peripherals, voltageregulators, power management circuits, and the like, which are wellknown in the art, and therefore, will not be described any further. Theprocessor may be implemented with one or more general-purpose and/orspecial-purpose processors. Examples include microprocessors,microcontrollers, DSP processors, and other circuitry that can executesoftware. Those skilled in the art will recognize how best to implementthe described functionality for the processing system depending on theparticular application and the overall design constraints imposed on theoverall system.

If implemented in software, the functions may be stored or transmittedover as one or more instructions or code on a computer-readable medium.Software shall be construed broadly to mean instructions, data, or anycombination thereof, whether referred to as software, firmware,middleware, microcode, hardware description language, or otherwise.Computer-readable media include both computer storage media andcommunication media including any medium that facilitates transfer of acomputer program from one place to another. The processor may beresponsible for managing the bus and general processing, including theexecution of software modules stored on the machine-readable storagemedia. A computer-readable storage medium may be coupled to a processorsuch that the processor can read information from, and write informationto, the storage medium. In the alternative, the storage medium may beintegral to the processor. By way of example, the machine-readable mediamay include a transmission line, a carrier wave modulated by data,and/or a computer readable storage medium with instructions storedthereon separate from the wireless node, all of which may be accessed bythe processor through the bus interface. Alternatively, or in addition,the machine-readable media, or any portion thereof, may be integratedinto the processor, such as the case may be with cache and/or generalregister files. Examples of machine-readable storage media may include,by way of example, RAM (Random Access Memory), flash memory, ROM (ReadOnly Memory), PROM (Programmable Read-Only Memory), EPROM (ErasableProgrammable Read-Only Memory), EEPROM (Electrically ErasableProgrammable Read-Only Memory), registers, magnetic disks, opticaldisks, hard drives, or any other suitable storage medium, or anycombination thereof. The machine-readable media may be embodied in acomputer-program product.

A software module may comprise a single instruction, or manyinstructions, and may be distributed over several different codesegments, among different programs, and across multiple storage media.The computer-readable media may comprise a number of software modules.The software modules include instructions that, when executed by anapparatus such as a processor, cause the processing system to performvarious functions. The software modules may include a transmissionmodule and a receiving module. Each software module may reside in asingle storage device or be distributed across multiple storage devices.By way of example, a software module may be loaded into RAM from a harddrive when a triggering event occurs. During execution of the softwaremodule, the processor may load some of the instructions into cache toincrease access speed. One or more cache lines may then be loaded into ageneral register file for execution by the processor. When referring tothe functionality of a software module below, it will be understood thatsuch functionality is implemented by the processor when executinginstructions from that software module.

Also, any connection is properly termed a computer-readable medium. Forexample, if the software is transmitted from a website, server, or otherremote source using a coaxial cable, fiber optic cable, twisted pair,digital subscriber line (DSL), or wireless technologies such as infrared(IR), radio, and microwave, then the coaxial cable, fiber optic cable,twisted pair, DSL, or wireless technologies such as infrared, radio, andmicrowave are included in the definition of medium. Disk and disc, asused herein, include compact disc (CD), laser disc, optical disc,digital versatile disc (DVD), floppy disk, and Blu-ray® disc where disksusually reproduce data magnetically, while discs reproduce dataoptically with lasers. Thus, in some aspects computer-readable media maycomprise non-transitory computer-readable media (e.g., tangible media).In addition, for other aspects computer-readable media may comprisetransitory computer-readable media (e.g., a signal). Combinations of theabove should also be included within the scope of computer-readablemedia.

Thus, certain aspects may comprise a computer program product forperforming the operations presented herein. For example, such a computerprogram product may comprise a computer-readable medium havinginstructions stored (and/or encoded) thereon, the instructions beingexecutable by one or more processors to perform the operations describedherein.

Further, it should be appreciated that modules and/or other appropriatemeans for performing the methods and techniques described herein can bedownloaded and/or otherwise obtained by a wireless node and/or basestation as applicable. For example, such a device can be coupled to aserver to facilitate the transfer of means for performing the methodsdescribed herein. Alternatively, various methods described herein can beprovided via storage means (e.g., RAM, ROM, a physical storage mediumsuch as a compact disc (CD) or floppy disk, etc.), such that a wirelessnode and/or base station can obtain the various methods upon coupling orproviding the storage means to the device. Moreover, any other suitabletechnique for providing the methods and techniques described herein to adevice can be utilized.

It is to be understood that the claims are not limited to the preciseconfiguration and components illustrated above. Various modifications,changes and variations may be made in the arrangement, operation anddetails of the methods and apparatus described above without departingfrom the scope of the claims.

What is claimed is:
 1. A method for wireless communications comprising:encoding a set of information bits based on a low-density parity-check(LDPC) code to produce a code word, the LDPC code defined by a basegraph having a first number of variable nodes and a second number ofcheck nodes; puncturing bits in the code word corresponding to at leasttwo of the first number of variable nodes in the base graph to produce apunctured code word, wherein the base graph includes at least oneadditional variable node for the at least two punctured variable nodes,and wherein each additional variable node is connected to one checknode, the check node coupled to a pair of punctured variable nodes; andtransmitting a signal associated with the punctured code word.
 2. Themethod of claim 1, wherein the at least two punctured variable nodeshave a higher degree of connectivity to the check nodes than the othervariable nodes in the base graph.
 3. The method of claim 1, wherein theat least two punctured variable nodes comprise M variable nodes, andwherein the at least one additional variable node comprises M−1 variablenodes.
 4. The method of claim 1, wherein the first number of variablenodes is 27 or 28 variable nodes.
 5. The method of claim 1, wherein theat least two punctured variable nodes have a first degree ofconnectivity to the check nodes that is lower than a second degree ofconnectivity of a variable node in a reference LDPC code.
 6. The methodof claim 1, further comprising generating at least one lifted LDPC codeby taking Z copies of the LDPC code defined by the base graph with theat least two punctured variable nodes and the at least one additionalvariable node.
 7. An apparatus comprising: means for encoding a set ofinformation bits based on a low-density parity-check (LDPC) code toproduce a code word, the LDPC code defined by a base graph having afirst number of variable nodes and a second number of check nodes; meansfor puncturing bits in the code word corresponding to at least two ofthe first number of variable nodes in the base graph to produce apunctured code word, wherein the base graph includes at least oneadditional variable node for the at least two punctured variable nodes,and wherein each additional variable node is connected to one checknode, the check node coupled to a pair of punctured variable nodes; andmeans for transmitting a signal associated with the punctured code word.8. The apparatus of claim 7, wherein the at least two punctured variablenodes have a higher degree of connectivity to the check nodes than theother variable nodes in the base graph.
 9. The apparatus of claim 7,wherein the at least two punctured variable nodes comprise M variablenodes, and wherein the at least one additional variable node comprisesM−1 variable nodes.
 10. The apparatus of claim 7, wherein the firstnumber of variable nodes is 27 or 28 variable nodes.
 11. The apparatusof claim 7, wherein the at least two punctured variable nodes have afirst degree of connectivity to the check nodes that is lower than asecond degree of connectivity of a variable node in a reference LDPCcode.
 12. The apparatus of claim 7, further comprising: means forgenerating at least one lifted LDPC code by taking Z copies of the LDPCcode defined by the base graph with the at least two punctured variablenodes and the at least one additional variable node.
 13. An apparatuscomprising: at least one processor coupled with a memory and configuredto: encode a set of information bits based on a low-density parity-check(LDPC) code to produce a code word, the LDPC code defined by a basegraph having a first number of variable nodes and a second number ofcheck nodes; puncture bits in the code word corresponding to at leasttwo of the first number of variable nodes in the base graph to produce apunctured code word, wherein the base graph includes at least oneadditional variable node for the at least two punctured variable nodes,and wherein each additional variable node is connected to one checknode, the check node coupled to a pair of punctured variable nodes; andtransmit a signal associated with the punctured code word.
 14. Theapparatus of claim 13, wherein the at least two punctured variable nodeshave a higher degree of connectivity to the check nodes than the othervariable nodes in the base graph.
 15. The apparatus of claim 13, whereinthe at least two punctured variable nodes comprise M variable nodes, andwherein the at least one additional variable node comprises M−1 variablenodes.
 16. The apparatus of claim 13, wherein the first number ofvariable nodes is 27 or 28 variable nodes.
 17. The apparatus of claim13, wherein the at least two punctured variable nodes have a firstdegree of connectivity to the check nodes that is lower than a seconddegree of connectivity of a variable node in a reference LDPC code. 18.The apparatus of claim 13, wherein the at least one processor is furtherconfigured to: generate at least one lifted LDPC code by taking Z copiesof the LDPC code defined by the base graph with the at least twopunctured variable nodes and the at least one additional variable node.19. A non-transitory computer readable medium having computer executablecode stored thereon comprising: code for encoding a set of informationbits based on a low-density parity-check (LDPC) code to produce a codeword, the LDPC code defined by a base graph having a first number ofvariable nodes and a second number of check nodes; code for puncturingbits in the code word corresponding to at least two of the first numberof variable nodes in the base graph to produce a punctured code word,wherein the base graph includes at least one additional variable nodefor the at least two punctured variable nodes, wherein each additionalvariable node is connected to one check node, the check node coupled toa pair of punctured variable nodes; and code for transmitting a signalassociated with the punctured code word.
 20. The non-transitory computerreadable medium of claim 19, wherein the at least two punctured variablenodes have a higher degree of connectivity to the check nodes than theother variable nodes in the base graph.
 21. The non-transitory computerreadable medium of claim 19, wherein the at least two punctured variablenodes comprise M variable nodes, and wherein the at least one additionalvariable node comprises M−1 variable nodes.
 22. The non-transitorycomputer readable medium of claim 19, wherein the first number ofvariable nodes is 27 or 28 variable nodes.
 23. The non-transitorycomputer readable medium of claim 19, wherein the at least two puncturedvariable nodes have a first degree of connectivity to the check nodesthat is lower than a second degree of connectivity of a variable node ina reference LDPC code.
 24. The non-transitory computer readable mediumof claim 19, further comprising: code for generating at least one liftedLDPC code by taking Z copies of the LDPC code defined by the base graphwith the at least two punctured variable nodes and the at least oneadditional variable node.